Gravity Model for Migration Stock

[Anastasia Simmonds]

Joao Santos Silva

Hi Professor,

I am estimating a Gravity Model using PPML, for my undergraduate dissertation. I am trying to estimate the effect of an increase in the CPI (a corruption measure) in the Origin country on the Total Migration Stock (TotMig). I expect that an increase in CPI will lead to an increase in the TotMig. But there is a concave relationship, so I have added a squared CPI term.
Independent variable: TotMig (not logged).
Dependent variables (not logged): OriginCPI, OriginCPI2, Contig, Colony
Dependent variables (logged): Distance, OriginGDP, DestinationGDP, OriginPopulation, DestinationPopulation

I have a few questions:
1. What fixed effects do you suggest I use? I was thinking of Origin, Destination, and Time fixed effects, and I will use ppml hdfe.
2. Do I need to log the OriginCPI or OriginCPI2 term?
3. How do I interpret the coefficients? I have 0.968OriginCPI - 0.107OriginCPI2 + ... . If there wasn't a squared term, I would just say that a 1% increase in OriginCPI leads to a 100(exp(0.968)-1)=163% increase in TotMig.


Thank you very much, I would really appreciate the help!

Anastasia

[Joao Santos Silva]

Dear Anastasia Simmonds,

First of all, I suppose that TotMig is you dependent variable, and the others are your regressors, right? Also, it would have been useful to say a bit more about the data, especially the dimension of the sample.

1 .For trade applications, there is a well established set of fixed effects that are used; these are motivated by economic theory. I do not thin that the same thing happens for migration, so you have a bit of freedom there and it is up to you to decide what is the best approach. Keep in mind that, if CPI has little variation over time, including origin fixed effects will not allow you to estimate the CPI coefficient precisely. So, you may need to see if it is feasible to include this type of fixed effects. Also, you may want to include pair-FE and time-FE, but again it is up to you to choose and you should be able to justify your choices carefully.

2. I do not know what that variable looks like, so it is difficult to advise on this. I do not think there is a right and a wrong way to proceed, so it is again up to you.

3. Without the square term, the interpretation would be that 1 unit increase (not 1%) in OriginCPI leads to a 100(exp(0.968)-1)=163% increase in the expected value of TotMig. With the square, the interpretation is the same but what you put in the exponential depends on the value of CPI (I think it is 0.968 - 0.107 - 2*0.107OriginCPI), but please check.

In any case, you should discuss all of this with your advisor.

Best wishes,

Joao

[Anastasia Simmonds]

Thank you, Professor, this helps a lot!

You are correct; I did mean that TotMig is my dependent variable and the others are the regressors.
Here is a bit more information about my data:
- I have 15 Origin countries (Eastern European), 20 Destination countries (OECD), and 3 time periods (2000, 2005 and 2010)
- CPI is a variable that takes on values 0-10. 0 means no corruption and 10 means totally corrupt.
- TotMig is the total migration stock of people from an Origin country in a Destination country.
- There are 900 observations in total

1. CPI has some variation over time. For example, Origin countries often experience changes of around 0.5 or 1 from period to period.
From what I understood from other posts in the forum, I should not use country-pair fixed effects, as I am already controlling for Distance (so there would be collinearity). Is this correct?

2. Since CPI is a variable that takes on values 0-10, would it make sense to log it? I remember reading in the forums that all non-dummy variables in a gravity model should be logged.

3. Thank you, I think this interpretation is correct! I will proceed to use the squared CPI term, as previous literature also has.

I really appreciate all of your contributions in the forum, they have really helped me understand gravity models and PPML much better.

Best wishes,
Anastasia

[Joao Santos Silva]

Dear Anastasia Simmonds,

Thanks for the additional information.

1. If you use pair-FE you will not be able to estimate the effect of distance, but you will be controlling for any pair-specific factors that are constant over your sample period. So, it is your call.

2. If you log it, the coefficient will be an elasticity, but I do not think that makes much sense because the response to a 1% increase in CPI does not appear to be an interesting thing to know, and you cannot log it anyway if it takes the value 0.

Best wishes,

Joao

[Anastasia Simmonds]

Hi Joao Santos Silva


Thank you for all your help!
I have been reading up on FEs, and decided not to use origin-FEs or destination-FEs, as the majority of my variables (including CPI) are pretty time-invariant for my time period 2000 - 2010. I believe that my model mostly exploits the variation in CPI between the origin countries, rather than the change in CPI over time. I am therefore including only time FEs.

I have read about random-intercept PPML models, which may be an alternative solution, however I do not know how to implement it in Stata. Is there a specific command for this?

Finally, how do I perform a RESET test on my PPML model? Is this the preferred way to test for omitted variable bias in PPML models?

Best wishes,
Anastasia

[Joao Santos Silva]

Dear Anastasia Simmonds,

I would not use random-intercept Poisson models (they cannot really be called PPML) because as far as I understand you would need to specify a distribution for the random intercepts, and we have no information on that.

You can see an example of how to perform a RESET test here, but note that the RESET is not a test for omitted variables, it is a functional form test.

Best wishes,

Joao